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2 years ago

Write the equation for g (x)

Mathematics

1 answer:

alisha [4.7K]2 years ago

5 0

By taking advantage of characteristics between two parallel lines we conclude that the linear equation parallel to f(x) is g(x) = -(4/17) · x + 455/17.

<h3>How to determine the equation of a line parallel to another line</h3>

In accordance with the analytical geometry, two lines are parallel when they share the same slope (m) but different intercepts (b). Linear functions are usually are described by the following form:

y = m · x + b (1)

Where:

x - Independent variable
y - Dependent variable

Based on the given information, we conclude that g(x) has a slope of -4/17. Lastly, we use (1) and the given point to determine the intercept of the function:

27 = -(4/17) · (-1) + b

b = 455/17

By taking advantage of characteristics between two parallel lines we conclude that the linear equation parallel to f(x) is g(x) = -(4/17) · x + 455/17.

To learn more on linear functions: brainly.com/question/21107621

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lilavasa [31]

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3 years ago

A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a day waiting period to purchase

il63 [147K]

Answer:

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

Step-by-step explanation:

The question is incomplete. The complete question is:

"A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?” Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes”. Use this information to find a 90% confidence interval for the difference in the two proportions, pm - pw. Subscript pm is the proportion of men who support the proposed law and pw is the proportion of women who support the proposed law. (Round answers to 3 decimal places.)"

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample of men, of size nm=-0.26 has a proportion of pm=0.612.

$p_m=X_m/n_m=318/520=0.612$

The sample 2, of size nw= has a proportion of pw=0.824.

$p_w=X_w/n_w=379/460=0.824$

The difference between proportions is (pm-pw)=-0.212.

$p_d=p_m-p_w=0.612-0.824=-0.212$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_m+X_w}{n_m+n_w}=\dfrac{318+379}{520+460}=\dfrac{697}{980}=0.711$

The estimated standard error of the difference between means is computed using the formula:

$s_{pm-pw}=\sqrt{\dfrac{p(1-p)}{n_m}+\dfrac{p(1-p)}{n_w}}=\sqrt{\dfrac{0.711*0.289}{520}+\dfrac{0.711*0.289}{460}}\\\\\\s_{pm-pw}=\sqrt{0.00039+0.00045}=\sqrt{0.001}=0.029$

Then, the margin of error is:

$MOE=z \cdot s_{pm-pw}=1.645\cdot 0.029=0.0477$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.212-0.0477=-0.260\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.212+0.0477=-0.165$

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

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3 years ago